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Question:

A straight wire carrying a current of 5A is bent into a semicircular arc of radius 2cm as shown in the figure. Find the magnitude and direction of the magnetic field at the center of the arc.

Solution:

For time elements ABCD, field = 0 because the distance between the wire and point P = zero.
Due to semi-circular element:
B = Bcomplete loop/2 = (µ₀I/2R)/2 [in the inward direction X]
µ₀ = 4π × 10⁻⁷
π = 3.14
I = 5 A
R = 2 × 10⁻² m
B = (10⁻⁷ × 3.14 × 5)/(2 × 10⁻²) = 7.85 × 10⁻⁵ T